Tampa, Florida (CNN) -- The U.S. military does not intend to put ground troops in Yemen, a country where al Qaeda operatives have become an increasing threat, Gen. David Petraeus told CNN in an interview to be aired Sunday.

However, the United States plans to more than double its security assistance funding to Yemen, from $70 million to more than $150 million, Petraeus, head of U.S. Central Command, told CNN's Christiane Amanpour at CENTCOM headquarters in Tampa.

Petraeus, who recently returned from his visit to the Arab nation, said Yemen's foreign minister was "quite clear that Yemen does not want to have American ground troops there. And that's a good -- good response for us to hear, certainly."

Asked on whether there were plans to send troops there, he replied, "No, of course, we would always want a host nation to deal with a problem itself. We want to help. We're providing assistance."

The United States also will provide additional economic aid to Yemen, the heel of the Arabian Peninsula that has also become known for its large ungoverned spaces that provide an oasis to terrorist groups. In addition to U.S. funds, Saudi Arabia reportedly has allocated $2 billion and the United Arab Emirates about $600 million or $700 million, all to help the Yemen government fight terror and promote development within its borders, according to Petraeus.

After the botched Christmas Day attack on a U.S.-bound airliner, Yemen-based al Qaeda in the Arabian Peninsula claimed responsibility, saying the attack was in retaliation for U.S. cruise missile strikes on its camps.

U.S. officials, speaking on condition of anonymity, have acknowledged providing intelligence on al Qaeda targets to Yemeni authorities, but won't say whether U.S. aircraft or ordnance played any role in the strikes.

"Again, we haven't discussed the assistance that we have provided in Yemen, and I'm afraid I won't here today," he said.

The general said the United States has been concerned about al Qaeda in the Arabian Peninsula for several years, saying, "Without question, it has ramped up over the course of the last year or more in particular, with training camps and so forth there."

Still, in comments made off camera, Petraeus said the group "isn't industrial strength."

Yemen President Ali Abdullah Saleh has told the United States that Yemen rather handle al Qaeda on its own, and the United States plans to honor that, Petraeus said.

We would always want a host nation to deal with a problem itself. ... We're providing assistance.
--Gen. David Petraeus, head of U.S. Central Command

"It threatened the embassies of various countries that are important to Yemen and, in fact, assassinated some government officials," Petraeus said, referring to the al Qaeda branch in Yemen. "So there is an enormous incentive here for President Saleh and the government of Yemen, indeed, to confront al Qaeda in the Arabian Peninsula and the growth that we have seen in its training camp structure and the other infrastructure that they've been able to establish in recent years."

Petraeus said al Qaeda's growth in Yemen became increasingly worrisome for him two years ago. Washington began to view the ancestral home of al Qaeda founder Osama bin Laden as a possible haven for the group as early as 2001.

As al Qaeda was pushed out of Saudi Arabia -- and under pressure in Iraq, Pakistan and Afghanistan -- they took refuge in Yemen, he said.

Last Sunday, the United States decided to briefly close its embassy in Yemen after intelligence suggested that four al Qaeda operatives may be planning an attack on the compound. The embassy reopened Tuesday. Britain, too, closed its embassy Sunday, citing security concerns, while other foreign embassies beefed up security or closed to the public.

Yet, Petraeus said Yemen is not the most important locale in the U.S. war on terror. "That would likely still be the western Pakistan-Afghanistan border area," he said.

"We have not devoted the kind of resources to it that is necessary. I know what it takes. We built an intelligence structure, we built an entire organization overall in Iraq to conduct counterinsurgency operations. And it requires a significant commitment.

"We are now making that kind of commitment to Afghanistan, but we had not before."

The general added that strides have been made in the fight against terrorists.

"I think there's been progress overall over the course of the last year against al Qaeda," Petraeus said. "I think that in general its capability has diminished, but that's only, again, a relative judgment ... Al Qaeda does still have an ability there to carry out periodic horrific attacks, and so we must maintain the pressure on Al Qaeda wherever it is found."